Warp-based helical implicit primitives

Implicit modeling with skeleton-based primitives has been limited up to now to planar skeleton elements, since no closed-form solution was found for convolution along more complex curves. We show that warping techniques can be adapted to efficiently generate convolution-like implicit primitives of varying radius along helices, a useful 3D skeleton found in a number of natural shapes. Depending on a single parameter of the helix, we warp it onto an arc of circle or onto a line segment. For those latter skeletons closed-form convolutions are known for entire families of kernels. The new warps introduced preserve the circular shape of the normal cross section to the primitive.

Graphical AbstractFigure optionsDownload full-size imageDownload high-quality image (36 K)Download as PowerPoint slideHighlights► Implicit modeling with skeleton-based primitives has been limited up to now to planar skeletons, since no closed-form solution was found for convolution along more complex curves. ► We show that warping techniques can be adapted to efficiently generate convolution-like implicit primitives of varying radius along helices–a very useful 3D skeleton found in a number of natural shapes. ► Depending on parameters, we either warp the helix onto an arc of circle or onto a line segment, on which closed-form convolution with arbitrary kernel is used. ► This is done by introduction a new familly of warps that restore a circular shape to the cross section of the primitive.